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Mathematics > Probability

Title:
Valuations and Boolean Models

Abstract: Valuations, as additive functionals, allow various applications in Stochastic
Geometry, yielding mean value formulas for specific random closed sets and
processes of convex or polyconvex particles. In particular, valuations are
especially adapted to Boolean models, the latter being the union sets of
Poisson particle processes. In this chapter, we collect mean value formulas for
scalar- and tensor-valued valuations applied to Boolean models under quite
general invariance assumptions.

Comments:

34 pages, to appear in Lecture Notes in Mathematics `Tensor Valuations and their Applications in Stochastic Geometry and Imaging'